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The graph provided represents a quadratic function, which is a parabola opening downwards. We can determine the **range** of this function by analyzing the graph.

### Key Observations:
- The **vertex** of the parabola is at the highest point, located at \((1, 5)\).
- Since the parabola opens downward, the range includes all \(y\)-values less than or equal to 5.

### Range of the Function:
- The range is all \(y\)-values such that \( y \leq 5 \).
- In interval notation, the range is \( (-\infty, 5] \).

Therefore, the correct answer choice should reflect that the range of the function \(r\) is \( (-\infty, 5] \).

Would you like further details, or do you have any questions?

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Here are 5 related questions to further your understanding:

1. How do you determine the vertex of a quadratic function from its graph?
2. What does the range of a function represent?
3. How can you tell if a parabola opens upwards or downwards from the graph?
4. How would the graph and range change if the parabola opened upwards?
5. How do you calculate the domain of a quadratic function?

**Tip**: The range of a quadratic function depends heavily on whether the parabola opens upward or downward, and this is determined by the sign of the coefficient of \(x^2\).

The graph of quadratic function r is shown on the grid. Which answer choice best represents the range of r?

Understand how to find the range of a quadratic function by analyzing the graph of a parabola. This problem includes key concepts of quadratic equations and their range, based on whether the parabola opens upwards or downwards. Suitable for Grades 8-10.

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